Combining Texts

All the ideas for 'Science and Method', 'On Recent German Literature. Fragments' and 'On boundary numbers and domains of sets'

expand these ideas     |    start again     |     specify just one area for these texts

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5 ideas

1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis

20947

Thoughts are learnt through words, so language shows the limits and shape of our knowledge [Herder]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

17832

Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII

13028

Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy]

5. Theory of Logic / L. Paradox / 3. Antinomies

17626

The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo]

6. Mathematics / A. Nature of Mathematics / 2. Geometry

10245

One geometry cannot be more true than another [Poincaré]